Geodesic
Special cases of the theory of multiple trigonometric sums
Izvestiya. Mathematics , Tome 23 (1984) no. 1, pp. 17-82.

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Estimates are proved for multiple trigonometric sums and the mean value of such sums under the condition that the variables of summation are very different from one another. Bibliography: 5 titles. 
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G. I. Arkhipov; A. A. Karatsuba; V. N. Chubarikov. Special cases of the theory of multiple trigonometric sums. Izvestiya. Mathematics , Tome 23 (1984) no. 1, pp. 17-82. http://geodesic.mathdoc.fr/item/IM2_1984_23_1_a1/

[1] Vinogradov I. M., Izbrannye trudy, AN SSSR, M., 1952 | MR | Zbl

[2] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., Kratnye trigonometricheskie summy, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 151, 1980 | MR | Zbl

[3] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., “Trigonometricheskie summy i ikh prilozheniya”, Izv. AN SSSR. Ser. matem., 44:4 (1980), 723–781 | MR | Zbl

[4] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., “Trigonometricheskie integraly”, Izv. AN SSSR. Ser. matem., 43:5 (1979), 971–1003 | MR | Zbl

[5] Vinogradov I. M., Metod trigonometricheskikh summ v teorii chisel, Nauka, M., 1980 | MR